A garden is in the shape of an isosceles right triangle. The length of the hypotenuse is 24 feet. What is the area of the triang
le?
1 answer:
Answer:
Area = 144 ft^2
Step-by-step explanation:
Remark
Use the Pythagorean theorem to find the length of the legs. Then multiply them together and divide by 2.
Equations
a^2 + a^2 = c^2
Area = (1/2) * a^2
Givens
c = 24
Solution
Remember that an isosceles triangle has 2 equal sides. Both legs of the triangle are equal to a.
a^2 + a^2 = c^2 Combine
2a^2 = 24^2 Expand
2a^2 = 576 Divide by 2
2a^2/2= 576/2
a^2 = 288 You might just as well leave this. go to area
Area = 1/2 (288)
Answer: Area = 144 ft^2
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Step-by-step explanation:
![\bf \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\ -----------------------------\\\\ \cfrac{s^3}{s^3}\implies \cfrac{216}{1000}\implies \cfrac{\sqrt[3]{216}}{\sqrt[3]{1000}}\implies \cfrac{s}{s}\impliedby \textit{similarity ratio}](https://tex.z-dn.net/?f=%5Cbf%20%5Ccfrac%7B%5Ctextit%7Bsimilar%20shape%7D%7D%7B%5Ctextit%7Bsimilar%20shape%7D%7D%5Cqquad%20%5Ccfrac%7Bs%7D%7Bs%7D%3D%5Ccfrac%7B%5Csqrt%7Bs%5E2%7D%7D%7B%5Csqrt%7Bs%5E2%7D%7D%3D%5Ccfrac%7B%5Csqrt%5B3%5D%7Bs%5E3%7D%7D%7B%5Csqrt%5B3%5D%7Bs%5E3%7D%7D%5C%5C%5C%5C%0A-----------------------------%5C%5C%5C%5C%0A%5Ccfrac%7Bs%5E3%7D%7Bs%5E3%7D%5Cimplies%20%5Ccfrac%7B216%7D%7B1000%7D%5Cimplies%20%5Ccfrac%7B%5Csqrt%5B3%5D%7B216%7D%7D%7B%5Csqrt%5B3%5D%7B1000%7D%7D%5Cimplies%20%5Ccfrac%7Bs%7D%7Bs%7D%5Cimpliedby%20%5Ctextit%7Bsimilarity%20ratio%7D)
and simplify it away
