Question
In a right-angled triangle, the length of the hypotenuse is 25 cm, and the perimeter is 60
cm. Find the area of the triangle.
Solution
Let the sides of the right-angled triangle be a, b, and the hypotenuse c = 25 cm. Given: Perimeter = a + b + c = 60, so a + b + 25 = 60, a + b = 35. Using Pythagoras' theorem: a² + b² = 25² = 625 Now, we solve the system of equations: a + b = 35 a² + b² = 625 Squaring a + b = 35, we get: (a + b)² = 35² = 1225 a² + 2ab + b² = 1225 625 + 2ab = 1225 2ab = 1225 - 625 = 600 ab = 300 Area = 1/2 × ab = 1/2 × 300 = 150 cm² Correct option: B) 150 cm²
More Triangle Questions
- If perpendicular and base of a right-angle triangle is, 6 cm and 8 cm, respectively, then find the length of the shortest median of triangle.
- Calculate the altitude of an equilateral triangle having each side of length 10√3 cm.
- Two triangles DEF and XYZ are congruent to each other such that DE = 10 cm, YZ = 24 cm, and ∠DEF = ∠XYZ = 90⁰. Find the circumradius of ΔDEF.
- In triangle ABC, DE is drawn parallel to BC, meeting AB at D and AC at E. If AD : DB = 3 : 2 and the area of triangle ADE is 45 cm², find: (a) the area of...
- If the inradius of a triangle with a perimeter of 60cm is 8 cm, then find the area of the triangle.(in cm2)
- Find the length of AC, if ΔABC ~ ΔRQP and BC = 21 cm, QP = 9 cm and RP = 15 cm.
- A △ ABC has sides 5 cm, 6 cm and 7 cm. AB extended touches a circle at P and AC extended touches the same circle at Q. Find the length (in cm) of AQ.
- Find the ratio between the area of an equilateral triangle with side 6 cm and the area of a square with side 6 cm.
- The inner-radius of a triangle is 5 cm, and the sum of lengths of its sides is 60 cm. What is the area of the triangle (in sq. cm.)?
- ∠A, ∠B, and∠C are three angles of ∆ABC.if ∠A-∠B=15°, ∠B-∠C =30°,then ∠ A, ∠B and ∠C are?
