Advertisements
Advertisements
प्रश्न
In a right-angled triangle ABC, if ∠B = 90°, AB - BC = 2 cm; AC - BC = 4 and its perimeter is 24 cm, find the area of the triangle.
Advertisements
उत्तर
Given, Perimeter of ΔABC = 24cm
⇒ AB + BC + AC = 24cm ....(i)
AB - BC = 2cm ....(ii)
AC - BC = 4cm ....(iii)
Adding (ii) and (iii), we get
AB + AC - 2BC = 6cm
⇒ AB + AC = 6 + 2BC ....(iv)
Substituing (iv) un (i), we get
6 + 2BC + BC = 24
⇒ 3BC = 18
⇒ BC = 6cm
⇒ AB = 2 + BC
= 2 + 6
= 8cm
∴ Area of right-angled ΔABC
= `(1)/(2) xx "BC" xx "AB"`
= `(1)/(2) xx 8 xx 6`
= 24cm2.
APPEARS IN
संबंधित प्रश्न
Find the area of an equilateral triangle of side 20 cm.
Find the area of the shaded region in the figure as shown, in which DPQS is an equilateral triangle and ∠PQR = 90°.
The area of an equilateral triangle is numerically equal to its perimeter. Find the length of its sides, correct two decimal places.
In a right-angled triangle PQR right-angled at Q, QR = x cm, PQ = (x + 7) cm and area = 30 cm2. Find the sides of the triangle.
Each equal side of an isosceles triangle is 3cm less than the unequal side. The height of the perpendicular from the vertex to the unequal side is 3cm less than the equal side. If the area of the isosceles triangle is 108cm2, find the perimeter of the triangle.
A wire when bent in the form of a square encloses an area of 16 cm2. Find the area enclosed by it when the same wire is bent in the form of an equilateral triangle
The cross-section of a canal is a trapezium in shape. If the canal is 10m wide at the top, 6m wide at the bottom and the area of cross-section is 72 sq.m, determine its depth.
If in an isosceles triangle, each of the base angles is 40°, then the triangle is ______.
In an isosceles triangle, angles opposite to equal sides are ______.
Two line segments are congruent, if they are of ______ lengths.
