Answer:
6m
6m
8m
Step-by-step explanation:
calm down ...
don't let a strange problem description overwhelm you right away.
always try to work with the things you know first. and only when you run into something you really don't know, start thinking.
so, perimeter.
your know, what a perimeter is ? it is the circumference. all the side lengths added together. the answer to "how much distance would you have to go, to walk all the way around it one time".
so, what is the circumference of the square based on what we know ?
well, it has 4 equal sides, right ? otherwise it would not be a square.
so, the perimeter is 4×(x+2) = 4x + 8
that is perfectly fine.
now to the next part we know.
the perimeter of the triangle is the sum of its 3 sides (otherwise it would not be a triangle).
an isoceles triangle is a special triangle that has 2 equal sides.
so, we actually know all 3 sides (at least relatively) :
x+3
x+5
and ... another
x+3 (because of the isoceles property)
so, the perimeter is
x + 3 + x + 3 + x + 5 = 3x + 11
alright.
and now we also know that both perimeters are of equal length.
what did that mean ?
that both expressions deliver the same result.
therefore,
4x + 8 = 3x + 11
aha !
x = 3
bingo !
therefore, the side lengths of the triangle are
x+3 = 3+3 = 6 (both sides in the top)
x+5 = 3+5 = 8
and that's all there is to it.
it is really not necessary to panic don't you think ?
![\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \qquad \qquad \sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}\\\\ -------------------------------\\\\ (4x^5\cdot x^{\frac{1}{3}})+(2x^4\cdot x^{\frac{1}{3}})-(7x^3\cdot x^{\frac{1}{3}})+(3x^2\cdot x^{\frac{1}{3}})\\\\+(9x^1\cdot x^{\frac{1}{3}})-(1\cdot x^{\frac{1}{3}}) \\\\\\ 4x^{5+\frac{1}{3}}+2x^{4+\frac{1}{3}}-7x^{3+\frac{1}{3}}+9x^{1+\frac{1}{3}}-x^{\frac{1}{3}}](https://tex.z-dn.net/?f=%5Cbf%20a%5E%7B%5Cfrac%7B%7B%20n%7D%7D%7B%7B%20m%7D%7D%7D%20%5Cimplies%20%20%5Csqrt%5B%7B%20m%7D%5D%7Ba%5E%7B%20n%7D%7D%20%5Cqquad%20%5Cqquad%0A%5Csqrt%5B%7B%20m%7D%5D%7Ba%5E%7B%20n%7D%7D%5Cimplies%20a%5E%7B%5Cfrac%7B%7B%20n%7D%7D%7B%7B%20m%7D%7D%7D%5C%5C%5C%5C%0A-------------------------------%5C%5C%5C%5C%0A%284x%5E5%5Ccdot%20x%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%29%2B%282x%5E4%5Ccdot%20x%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%29-%287x%5E3%5Ccdot%20x%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%29%2B%283x%5E2%5Ccdot%20x%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%29%5C%5C%5C%5C%2B%289x%5E1%5Ccdot%20x%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%29-%281%5Ccdot%20x%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%29%0A%5C%5C%5C%5C%5C%5C%0A4x%5E%7B5%2B%5Cfrac%7B1%7D%7B3%7D%7D%2B2x%5E%7B4%2B%5Cfrac%7B1%7D%7B3%7D%7D-7x%5E%7B3%2B%5Cfrac%7B1%7D%7B3%7D%7D%2B9x%5E%7B1%2B%5Cfrac%7B1%7D%7B3%7D%7D-x%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D)
![\bf 4x^{\frac{16}{3}}+2x^{\frac{13}{3}}-7x^{\frac{10}{3}}+9x^{\frac{4}{3}}-x^{\frac{1}{3}} \\\\\\ 4\sqrt[3]{x^{16}}+2\sqrt[3]{x^{13}}-7\sqrt[3]{x^{10}}+9\sqrt[3]{x^4}-\sqrt[3]{x}](https://tex.z-dn.net/?f=%5Cbf%204x%5E%7B%5Cfrac%7B16%7D%7B3%7D%7D%2B2x%5E%7B%5Cfrac%7B13%7D%7B3%7D%7D-7x%5E%7B%5Cfrac%7B10%7D%7B3%7D%7D%2B9x%5E%7B%5Cfrac%7B4%7D%7B3%7D%7D-x%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%0A%5C%5C%5C%5C%5C%5C%0A4%5Csqrt%5B3%5D%7Bx%5E%7B16%7D%7D%2B2%5Csqrt%5B3%5D%7Bx%5E%7B13%7D%7D-7%5Csqrt%5B3%5D%7Bx%5E%7B10%7D%7D%2B9%5Csqrt%5B3%5D%7Bx%5E4%7D-%5Csqrt%5B3%5D%7Bx%7D)
![\bf 4x^{5-\frac{1}{3}}+2x^{4-\frac{1}{3}}-7x^{3-\frac{1}{3}}+9x^{1-\frac{1}{3}}-x^{-\frac{1}{3}} \\\\\\ 4x^{\frac{14}{3}}+2x^{\frac{11}{3}}-7x^{\frac{8}{3}}+9x^{\frac{2}{3}}-x^{-\frac{1}{3}} \\\\\\ 4\sqrt[3]{x^{14}}+2\sqrt[3]{x^{11}}-7\sqrt[3]{x^{8}}+9\sqrt[3]{x^{2}}-\frac{1}{\sqrt[3]{x}}](https://tex.z-dn.net/?f=%5Cbf%204x%5E%7B5-%5Cfrac%7B1%7D%7B3%7D%7D%2B2x%5E%7B4-%5Cfrac%7B1%7D%7B3%7D%7D-7x%5E%7B3-%5Cfrac%7B1%7D%7B3%7D%7D%2B9x%5E%7B1-%5Cfrac%7B1%7D%7B3%7D%7D-x%5E%7B-%5Cfrac%7B1%7D%7B3%7D%7D%0A%5C%5C%5C%5C%5C%5C%0A4x%5E%7B%5Cfrac%7B14%7D%7B3%7D%7D%2B2x%5E%7B%5Cfrac%7B11%7D%7B3%7D%7D-7x%5E%7B%5Cfrac%7B8%7D%7B3%7D%7D%2B9x%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D-x%5E%7B-%5Cfrac%7B1%7D%7B3%7D%7D%0A%5C%5C%5C%5C%5C%5C%0A4%5Csqrt%5B3%5D%7Bx%5E%7B14%7D%7D%2B2%5Csqrt%5B3%5D%7Bx%5E%7B11%7D%7D-7%5Csqrt%5B3%5D%7Bx%5E%7B8%7D%7D%2B9%5Csqrt%5B3%5D%7Bx%5E%7B2%7D%7D-%5Cfrac%7B1%7D%7B%5Csqrt%5B3%5D%7Bx%7D%7D)
![\bf \begin{cases} f(x)=\sqrt{x}-5x\implies &f(x)x^{\frac{1}{2}}-5x\\\\ g(x)=5x^2-2x+\sqrt[5]{x}\implies &g(x)=5x^2-2x+x^{\frac{1}{5}} \end{cases} \\\\\\ \textit{let's multiply the terms from f(x) by each term in g(x)} \\\\\\ x^{\frac{1}{2}}(5x^2-2x+x^{\frac{1}{5}})\implies x^{\frac{1}{2}}5x^2-x^{\frac{1}{2}}2x+x^{\frac{1}{2}}x^{\frac{1}{5}}](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Bcases%7D%0Af%28x%29%3D%5Csqrt%7Bx%7D-5x%5Cimplies%20%26f%28x%29x%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D-5x%5C%5C%5C%5C%0Ag%28x%29%3D5x%5E2-2x%2B%5Csqrt%5B5%5D%7Bx%7D%5Cimplies%20%26g%28x%29%3D5x%5E2-2x%2Bx%5E%7B%5Cfrac%7B1%7D%7B5%7D%7D%0A%5Cend%7Bcases%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Ctextit%7Blet%27s%20multiply%20the%20terms%20from%20f%28x%29%20by%20each%20term%20in%20g%28x%29%7D%0A%5C%5C%5C%5C%5C%5C%0Ax%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D%285x%5E2-2x%2Bx%5E%7B%5Cfrac%7B1%7D%7B5%7D%7D%29%5Cimplies%20x%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D5x%5E2-x%5E%7B%5Cfrac%7B1%7D%7B2%7D%7D2x%2Bx%5E%7B%5Cfrac%7B1%7D%7B2%7D%7Dx%5E%7B%5Cfrac%7B1%7D%7B5%7D%7D)
![\bf 5\sqrt{x^5}-2\sqrt{x^3}+\sqrt[10]{x^7}-25x^3+10x^2-5\sqrt[5]{x^6}](https://tex.z-dn.net/?f=%5Cbf%205%5Csqrt%7Bx%5E5%7D-2%5Csqrt%7Bx%5E3%7D%2B%5Csqrt%5B10%5D%7Bx%5E7%7D-25x%5E3%2B10x%5E2-5%5Csqrt%5B5%5D%7Bx%5E6%7D)
