-An apartment complex stretched a string of decorative floats diagonally across a rectangular pool. The width of the pool is 15 ft and the length of the pool is 20 ft.
What is the length of the a diagonal that the floats are stretched across?

answer: the first graph

step-by-step explanation:

< 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)

we need to divide the number of toy dinosaurs, 156, by the number of brothers, 4:

in order to estimate, we can use compatible numbers:

156 ÷ 4

  ↓

160   ÷ 4 = 40        

the correct answer is a).