ABC is an isosceles triangle with AB = AC = 12 cm and BC = 8 cm. Find the altitude on BC and hence calculate its area.

Let AD be altitude on BC and BD = x cm and CD = (8 - x) cm. From figure, In right angle △ABD, By pythagoras theorem, AB 2 = AD 2 + BD 2 12 2 = AD 2 + x 2 AD 2 = 12 2 - x 2 ........(i) In right angle △ADC, By pythagoras theorem, AC 2 = AD 2 + DC 2 12 2 = AD 2 + (8 - x) 2 AD 2 = 12 2 - (8 - x) 2 ........(ii) From (i) and (ii) we get, 12 2 - x 2 = 12 2 - (8 - x) 2 144 - x 2 = 144 - (64 + x 2 - 16x) 144 - x 2 = 144 - 64 - x 2 + 16x 144 - 144 - x 2 + x 2 + 64 = 16x 16x = 64 x = 4. Substituting value of x in (i) we get, AD 2 = 12 2 - x 2 = 144 - (4) 2 = 144 - 16 = 128 AD 2 = 128 AD = cm. Area = cm 2 . Hence, AD = cm and area = cm 2 .

Find the area and the perimeter of a square whose diagonal is 10 cm long.

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In a triangle ABC, AD is perpendicular to BC. Prove that AB² + CD² = AC² + BD².

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In △PQR, PD ⊥ QR such that D lies on QR. If PQ = a, PR = b, QD = c and DR = d, prove that (a + b)(a - b) = (c + d)(c - d).

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In figure given below, ABCD is a quadrilateral in which AD = 13 cm, DC = 12 cm, BC = 3 cm, ∠ABD = ∠BCD = 90°. Calculate the length of AB.

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Mathematics

ABC is an isosceles triangle with AB = AC = 12 cm and BC = 8 cm. Find the altitude on BC and hence calculate its area.

Pythagoras Theorem

Related Questions

Find the area and the perimeter of a square whose diagonal is 10 cm long.

In a triangle ABC, AD is perpendicular to BC. Prove that AB² + CD² = AC² + BD².

In △PQR, PD ⊥ QR such that D lies on QR. If PQ = a, PR = b, QD = c and DR = d, prove that (a + b)(a - b) = (c + d)(c - d).

In figure given below, ABCD is a quadrilateral in which AD = 13 cm, DC = 12 cm, BC = 3 cm, ∠ABD = ∠BCD = 90°. Calculate the length of AB.

Mathematics

ABC is an isosceles triangle with AB = AC = 12 cm and BC = 8 cm. Find the altitude on BC and hence calculate its area.

Pythagoras Theorem

Related Questions

Find the area and the perimeter of a square whose diagonal is 10 cm long.

In a triangle ABC, AD is perpendicular to BC. Prove that AB2 + CD2 = AC2 + BD2.

In △PQR, PD ⊥ QR such that D lies on QR. If PQ = a, PR = b, QD = c and DR = d, prove that (a + b)(a - b) = (c + d)(c - d).

In figure given below, ABCD is a quadrilateral in which AD = 13 cm, DC = 12 cm, BC = 3 cm, ∠ABD = ∠BCD = 90°. Calculate the length of AB.

In a triangle ABC, AD is perpendicular to BC. Prove that AB² + CD² = AC² + BD².