How do I solve for x?

Mathematics

2 answers:

PilotLPTM [1.2K]2 years ago

6 0

So it states that the area of the rectangle is 56 cm, so all of it.
Given: 56 cm of rectangle
Unknown: find x
Length: 2 + x or x + 2
Width: 2x-5
Area = l * w
(x+2)(2x-5)
set x equal to 0
x+2=0 --> x=-2 2x-5=0 --> 2x=5 --> x = 5/2
so the answer we got was x=-2,5/2
we know that x cannot be negative because you can't measure with negative numbers, therefore, 5/2 is your answer

iragen [17]2 years ago

4 0

Length = a
width = b

ab = 56 ---- first equation
a = 2 + x ---- second equation
b = 2x - 5 ---- third equation

substitude second and third equation into the first equation

(2+x)(2x-5) = 56
4x - 10 + 2x^2 - 5x = 56
2x^2 - x - 10 - 56 = 0
2x^2 - x - 66 = 0
(x-6)(2x+11) = 0
x1 = 6 , x2 = - 11/2 ---> - 5.5 (nearest whole num)

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2 years ago

Find the surface area of the following figure.

fgiga [73]

Answer:

$\boxed{\textsf{\pink{ Hence the TSA of the cuboid is $\sf 32x^2$}}}.$

Step-by-step explanation:

A 3D figure is given to us and we need to find the Total Surface area of the 3D figure . So ,

From the cuboid we can see that there are 5 squares in one row on the front face . And there are two rows. So the number of squares on the front face will be 5*2 = 10 .

We know the area of square as ,

$\qquad\boxed{\sf Area_{(square)}= side^2}$

Hence the area of 10 squares will be 10x² , where x is the side length of each square. Similarly there are 10 squares at the back . Hence their area will be 10x² .

Also there are in total 12 squares sideways 6 on each sides . So their surface area will be 12x² . Hence the total surface area in terms of side of square will be ,

$\sf\implies TSA_{(cuboid)}= 10x^2+10x^2+12x^2\\\\\sf\implies\boxed{\sf TSA_{(cuboid)}= 32x^2}$

Now let's find out the TSA in terms of side . So here the lenght of the cuboid is equal to the sum of one of the sides of 5 squares .

$\sf\implies 5x = l \\\\\sf\implies x = \dfrac{l}{5} \\\\\qquad\qquad\underline\red{ \sf Similarly \ breadth }\\\\\sf\implies b = 3x \\\\\sf\implies x = \dfrac{ b}{3}$

$\rule{200}2$

Hence the TSA of cuboid in terms of lenght and breadth is :-

$\sf\implies TSA_{(cuboid)}= 10x^2+10x^2+12x^2\\\\\sf\implies TSA_{(cuboid)}= 20\bigg(\dfrac{l}{5}\bigg)^2+12\bigg(\dfrac{b}{3}\bigg) \\\\\sf\implies TSA_{(cuboid)}= 20\times\dfrac{l^2}{25}+12\times \dfrac{b^2}{9}\\\\\sf\implies \boxed{\red{\sf TSA_{(cuboid)}= \dfrac{4}{5}l^2 +\dfrac{4}{3}b^2 }}$