Question

In the given figure, PQRS is a parallelogram, and T is the midpoint of RS. If the length of QT is 12cm, what will be the length of UT (in cm)?​

Answer 1

A quadrilateral ABCD with DC = 17 cm, AD = 9 cm and BC = 8 cm (Given)

In right ΔABD,

Using Pythagorean Theorem,

AB2 + AD2 = BD2

152 = AB2 + 92

AB2 = 225−81=144

AB = 12

Area of ΔABD = 1/2(12×9) cm2 = 54 cm2

In right ΔBCD:

Using Pythagorean Theorem,

CD2 = BD2 + BC2

172 = BD2 + 82

BD2 = 289 – 64 = 225

or BD = 15

Area of ΔBCD = 1/2(8×17) cm2 = 68 cm2

Now, area of quadrilateral ABCD = Area of ΔABD + Area of ΔBCD

= 54 cm2 + 68 cm2

= 112 cm2