What is the length of AC?

Question

asked Sep 2, 2019 190k views

2 Answers

ScarletAmaranth · Answer 1 · 2019-09-08T10:06:08+0000

In the given diagram, We are given two right triangles BAC and DEC.

Triangle BAC has right angle at A and triangle DEC has right angle at E.

Also we are given <BCA ≅<DCA.

Therefore,

Triangle BAC is similar to triangle DEC by Angle Angle similarity theorem.

Note: The sides of similar triangles are in proportion.

Therefore,

(AB)/(ED) = (AC)/(EC)

(84)/(7)=(156-x)/(x)

$\mathrm{Apply\:fraction\:cross\:multiply:\:if\:}(a)/(b)=(c)/(d)\mathrm{\:then\:}a\cdot \:d=b\cdot \:c$

$84x=7\left(156-x\right)$

84x=1092-7x

$\mathrm{Add\:}7x\mathrm{\:to\:both\:sides}$

84x+7x=1092-7x+7x

91x=1092

$\mathrm{Divide\:both\:sides\:by\:}91$

(91x)/(91)=(1092)/(91)

x=12

AC = 156 -x.

Plugging value of x in 156-x, we get

156-12 = 144.