# Difference between revisions of "2021 JMPSC Accuracy Problems/Problem 6"

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We note that triangle <math>ABC</math> and <math>DAC</math> are congruent due to <math>AA</math> congruency. Therefore, <math>AD + DC = 28</math> and the perimeter of the quadrilateral is <math>28+28 = \boxed{56}</math> | We note that triangle <math>ABC</math> and <math>DAC</math> are congruent due to <math>AA</math> congruency. Therefore, <math>AD + DC = 28</math> and the perimeter of the quadrilateral is <math>28+28 = \boxed{56}</math> | ||

+ | |||

+ | ~Grisham |

## Revision as of 12:54, 11 July 2021

## Problem

In quadrilateral , diagonal bisects both and . If and , find the perimeter of .

## Solution

Notice that since bisects a pair of opposite angles in quadrilateral , we can distinguish this quadrilateral as a kite.

With this information, we have that and .

Therefore, the perimeter is

~Apple321

## Solution 2

We note that triangle and are congruent due to congruency. Therefore, and the perimeter of the quadrilateral is

~Grisham