Question
The altitude drawn to the base of an isosceles triangle is 6 cm and the perimeter of the triangle is 36
The altitude drawn to the base of an isosceles triangle is 6 cm and the perimeter of the triangle is 36
cm. The area (in cm²) of the triangle is
Let AB = AC = a cm. BD = DC = b cm. Altitude of isosceles triangle is also median. In right ∆ADC, 6² = a² - b² 36 = a² - b² ………… (i) Perimeter = 36 a + a + 2b = 36 2a + 2b = 36 a + b = 18 ………. (ii) On dividing (i) & (ii) we get, (a² - b² )/(a+b) = 36/18 = 2 ((a+b) (a-b))/((a+b)) = 2 a – b = 2 a + b = 18 on solving, 2a = 20 a = 10 b = 8 BC = 16 Area of ∆ABC = 1/2 × AD × BC = 1/2 × 6 × 16 = 48 cm²More Geometry Questions
- If G is the centroid and AD, BE, CF are three medians of ∆ABC with area 42 cm 2 , then the area of ∆BGD is?
- The perimeter of a rectangular field is 240 meters, and its length is 20% more than its breadth. What is the area of the field?
- Find the ratio between the area of the in-circle and the circum-circle of a square?
- In ∆ABC , G is the centroid , AB = 5 cm, BC= 8 cm and AC = 7 cm , find GD, where D is the mid-point of BC?
- In triangle ABC, AB = AC. Point D lies on AB such that AD = DC = BC. Find the value of ∠BDC.
- The lengths of three medians in a triangles are 21 cm, 28 cm, 35 cm. What is the area of that traingle (in cm 2 )?
- Find the radius of the sphere whose volume is 562.5π cm3
- Question 8
- In ∆ABC , G is the centroid , AB = 18 cm, BC= 24 cm and AC = 30 cm , find GD, where D is the mid-point of BC?
- In ∆ABC, AB = 5cm, BC = 6cm and AC = 10cm then find out the value of cos A?
Relevant for Exams:
Hey! Ask a query
Please enter email id
The email must be a valid email address.
Please enter Mobile Number
Please enter valid Mobile Number
Please enter your Doubt
Think You're Ready for RBI Grade B?
RBI Grade B 2026 Phase 1 Memory Based Paper
- 200 Questions with Detailed Solutions
- Section-wise Coverage (GA, English, Quant & Reasoning)