the rectangle with a side of length 12cm has a diagonal of 15cm. what is the perimeter of the rectangle?

42 cm

Step-by-step explanation:

First since the second side length is unknow we need to find it.

We will use the Pythagorean theorem which is

Since we will be solving for b we will rearrange the equation to be

now to slove input the data we know

= 144 - 225

= 81

= 9

With the two sides we simply add up all the sides for the perimeter

9+12+9+12 = 42

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)