Prove that in an equilateral triangle- three time the square of a side is equal to four time the square of its altitude-

Question

Toppr Admin · Accepted Answer

Let side of an equilateral triangle - a-We kno that-In equilateral triangle of side a- the altitude of triangle -x221A-3a2-x2234-xA0- 4 x The square of altitude -4-xD7-x221A-3a2-2-3a2- three times square of a side-Hence proved-xA0-

Prove that in an equilateral triangle, three time the square of a side is equal to four time the square of its altitude.

Let side of an equilateral triangle = a,

We kno that,
In equilateral triangle of side $a$ , the altitude of triangle $= \frac{\sqrt{3} a}{2}$

$∴$ 4 x The square of altitude $= 4 \times {(\frac{\sqrt{3} a}{2})}^{2} = 3 a^{2} =$ three times square of a side.

Hence proved.

Prove that in an equilateral triangle, three time the square of a side is equal to four time the square of its altitude.

Let side of an equilateral triangle = a,We kno that,In equilateral triangle of side a, the altitude of triangle =√3a2∴ 4 x The square of altitude =4×(√3a2)2=3a2= three times square of a side.Hence proved.

Let side of an equilateral triangle = a,

We kno that,
In equilateral triangle of side $a$ , the altitude of triangle $= \frac{\sqrt{3} a}{2}$

$∴$ 4 x The square of altitude $= 4 \times {(\frac{\sqrt{3} a}{2})}^{2} = 3 a^{2} =$ three times square of a side.

Hence proved.