Right isosceles triangle with hypotenuse 20 cm – Find area:\nIn right triangle PQR, PQ = QR. If hypotenuse PR = 20 cm, find the area of ∆PQR.

Difficulty: Easy

100√2
100
50√2
50
None of these

Correct Answer: 100

Explanation:

Introduction / Context:
In a right isosceles triangle, hypotenuse = leg * √2. Area = (1/2) * leg^2.

Step-by-Step Solution:

Let each leg = a ⇒ hypotenuse = a√2 = 20 ⇒ a = 20/√2 = 10√2.Area = (1/2) * a^2 = 0.5 * (10√2)^2 = 0.5 * 200 = 100 sq cm.

Final Answer:
100

← Previous Question Next Question→

More Questions from Area

Square PQRS side 20 cm – Four triangles by joining opposite vertices:\nBy joining opposite vertices (i.e., both diagonals), the square is partitioned into four congruent triangles. Find the sum of the perimeters of the four triangles.
Square with external equilateral on a side – Find ∠BEC:\nABCD is a square; on side CD an equilateral triangle CDE is constructed externally. Find the measure of ∠BEC.
Annular path around a circular garden – Outer radius 21 + 3.5 m:\nA circular garden has radius 21 m. A path 3.5 m wide surrounds it outside. Find the area of the path (in m²).
Melted hemisphere forms a cylinder – Given CSA:TSA = 2:3, hemisphere radius 14 cm:\nA solid hemisphere of radius 14 cm is melted and cast into a cylinder. For the cylinder, curved surface area : total surface area = 2 : 3. Find the cylinder’s base radius (in cm).
Centroid segment length – Triangle XYZ with sides 11, 14, 7 cm:\nG is centroid and M is the midpoint of XY. Given XY = 11 cm, YZ = 14 cm, XZ = 7 cm. Find GM (in cm).
Square inscribed in a circle (radius 4 cm) with an external tangent:\nPQRS is a square inscribed in a circle of radius 4 cm (so the circle's diameter equals the square's diagonal). Side PQ is extended beyond Q to meet a point Y. From Y, a tangent is drawn to the circle touching it at point R. Find the exact length (in cm) of segment SY.
Trapezium with intersecting diagonals split ratio 2:9:\nIn a trapezium, one diagonal divides the other in the ratio 2 : 9 at their intersection. If the longer parallel side is 45 cm, find the exact length (in cm) of the other parallel side.
Direct common tangent between two circles:\nThe distance between the centres is 61 cm, and the radii are 35 cm and 24 cm. Find the length (in cm) of a direct common tangent.
Angle-bisector area split inside a triangle:\nTriangle PQR has area 180 cm^2. Point S lies on QR, and PS is the angle bisector of ∠QPR. If PQ : PR = 2 : 3, find the area (in cm^2) of triangle PSR.
Nested mid-point squares inside a square and an inscribed circle:\nABCD is a square. EFGH is formed by joining midpoints of ABCD; LMNO is formed similarly from EFGH. A circle is inscribed in EFGH and has area 38.5 sq cm. Find the area (in sq cm) of square ABCD.

Discussion & Comments

No comments yet. Be the first to comment!

Join Discussion