A rectangle has area 48 cm² and perimeter 28 cm. If the midpoints of the sides are joined to form a rhombus, what is the area of the rhombus?
एक आयत का क्षेत्रफल 48 सेमी² और परिमाप 28 सेमी है। यदि आयत की भुजाओं के मध्य बिंदुओं को मिलाकर एक समचतुर्भुज बनाया जाए, तो समचतुर्भुज का क्षेत्रफल ज्ञात कीजिए।
This Question Asked In:
CGL MAINS 2026, SSC
Correct Answer :B - 24 cm²
Detailed Text Solution
Let length = l and breadth = b.
Given:
lb = 48
2(l + b) = 28 → l + b = 14
We know:
(l − b)² = (l + b)² − 4lb
= 14² − 4×48
= 196 − 192
= 4
So l − b = 2.
Solving:
l + b = 14
l − b = 2
Adding:
2l = 16 → l = 8
b = 6.
When midpoints of sides of a rectangle are joined, a rhombus is formed.
Area of such rhombus = half the area of rectangle.
Therefore,
Area = 48 / 2 = 24 cm².