Question

Help me I beg you

You will be cursed if you give me a nonsense answer
In △ABC a line segment
DE
connects sides
AB
and
BC
so that
DE
∥
AC
. The lengths of the sides of △DBE are four times shorter than the lengths of the sides of △ABC. What is the area of △ABC if the area of a trapezoid ADEC is 30cm2?

Answer 1

32

Explanation:

ratio of areas equal the ratio of corresponding sides squared (*)

ratio of corresponding sides of triangle ABC and triangle ADE = 4/1

area of triangle ADE will equal x, so then the area of triangle ABC will be x + 30 (bc the area of ADEC is 30, you just add that to x to get the area of ABC)

now let's set up our proportion:

Area of triangle ABC 4^2

--------------------------------- = ---------- <---- 4/1 is squared because of (*)

Area of triangle ADE 1^2

substitute:

A + 30 16

---------- = ----------

A 1

cross multiple to get A = 2, so then ABC = ADE + ADEC, which is 30 + 2 = 32

i did draw a diagram but after reviewing i drew it wrong so good luck drawing the diagram

also is this your 8th grade honors geometry math hw for RSM? HW 23 or something. if yes then oof.

comment if u have questions