Question

PQR is an isosceles triangle whose base QR =12 and each equal side is 10 .find the area if PM perpendicular QR and also find length of the perpendicular drawn from Q on PR

Answer 1

• qn=10.908
• approximately 11cm

Answer 2

Area of triangle is 48cm² and length of perpendicular is 8 cm

Step-by-step explanation:

Given : PQR is an isosceles triangle in which QR= 12 cm And PQ=PR=10 cm

Now PM is perpendicular to QR

Perpendicular of an isosceles triangle bisects the line

Therefore  

MR= 6 cm

PR= 10cm

Now using Pythagoras

In a right-angled triangle,  the square of the hypotenuse side is equal to the sum of squares of the other two sides

$PR^2= PM^2+MR^2\\\\\Rightarrow 10^2=PM^2+6^2\\\\\Rightarrow 100-36= PM^2\\\\\Rightarrow PM^2=64\\\\\Rightarrow PM= 8$

Now area of triangle is given by $area= \dfrac{1}{2} \times base \times height= \dfrac{1}{2} \times QR \times PM=\dfrac{1}{2} \times 12\times 8= 48 cm^2$

Area of triangle is 48cm² and length of perpendicular is 8 cm

#Learn more

State and prove Pythagoras theorem.

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