Question

ABCD is a parallelogram whose diagonals meet
at E. The perimeter of ABCD is 120 while the
perimeters of the triangles BCE and CDE differ by
40. Find sum of the squares of the diagonals of
ABCD.​

Answer 1

Answer:

ABCD is a parallelogram whose diagonals intersect each other at O with 90°.

so it's a rhombus as diagonals of rhombus interest each other at right angles.

diagonal1 (AC) = 6cm

diagonal 2(BD) = 8cm

OD = OB = 3cm each

OA = OC = 4cm each

Let, us take triangle AOB

it is a right angled triangle

=> (OA)² + (OB)² = (AB)²

=> (4)² + (3)² = (AB)²

=> 16 + 9 = (AB)²

=> 25 = (AB)²

=> = AB

=> 5 = AB

So, AB = 5cm

AB = BC = CD = AD (all sides of rhombus are equal)

Each side of the parallelogram ABCD is 5cm.