2021 JMPSC Accuracy Problems/Problem 6: Difference between revisions
Created page with "==Problem== In quadrilateral <math>ABCD</math>, diagonal <math>\overline{AC}</math> bisects both <math>\angle BAD</math> and <math>\angle BCD</math>. If <math>AB=15</math> and..." |
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==Solution== | ==Solution== | ||
Notice that since <math>\overline{AC}</math> bisects a pair of opposite angles in quadrilateral <math>ABCD</math>, we can distinguish this quadrilateral as a kite. | |||
<math>\linebreak</math> | |||
With this information, we have that <math>\overline{AD}=\overline{AB}=15</math> and <math>\overline{CD}=\overline{BC}=13</math>. | |||
Therefore, the perimeter is <cmath>15+15+13+13=\boxed{56}</cmath> | |||
<math>\square</math> | |||
<math>\linebreak</math> | |||
~Apple321 | |||
Revision as of 22:48, 10 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 ![\[15+15+13+13=\boxed{56}\]](http://latex.artofproblemsolving.com/1/b/1/1b1b1dcd079c7607c798a48296c33e99610609ae.png)
~Apple321
