Math, asked by polashigogoi40, 8 months ago

9. An isosceles triangle has its base of 20 cm and each of its equal sides is 26 cm long
Find out : (i) its height, (ii) its area.​

Answers

Answered by ravikumar555q
4

Answer:

(i) h = 16.61 cm

(ii) area = 166.1 cm²

Step-by-step explanation:

(i)

(height of triangle)² = (26)² - (20)² ( by Pythagoras)

(h)² = 676 - 400

h = √276

h = 16.61 cm

so,

(ii) Area of triangle = 1/2( b × h )

= 1/2 ( 20 × 16.61 )

= 166.1 cm²

Answered by EnchantedBoy
6

Answer:

(i)Height:

Consider an Isosceles triangle ABC, withAB=AC=26cm,BC=20cm

Draw a perpendicular AD on non-congruent side BC

In an Isosceles triangle a perpendicular bisects then non-congruent side

Hence, BD=\frac{1}{2} BC=\frac{1}{2}(20)=10cm

In ΔABD,

⇒AB^{2}=AD^{2}+BD^{2}

⇒26^{2}=AD^{2}+10^{2}

⇒676=AD^{2}=100

⇒AD^{2}=100-676

⇒AD^{2}=576

⇒AD=\sqrt{576}

⇒AD=24cm

(ii)Area:

First find out It's height by Pythagoras theorem,

⇒c^{2}=a^{2}+b^{2}

⇒26^{2}=10^{2}+b^{2}

⇒576=b^{2}

⇒b^{2}=576

⇒b=\sqrt{576}

⇒b=24

Now  area=base×height

⇒20×24

⇒480cm^{2}

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