The base of a triangle is seven more than twice the height. the area of a triangle is 186 yd.² find the measure of the base in the height of the triangle

The height of Triangle is 12 yd      and

The base of Triangle is 31 yd

Step-by-step explanation:

Given as :

The area of triangle = 186 yd²

Let the height of triangle = h

So, base of triangle = 7 + 2 h

Now,

∵ The area of triangle =

Or,  186 yd² =  

Or,  186 × 2 = h × ( 7 +2h )

Or,  372 = 7 h + 2 h²

Or,  2 h² + 7 h - 372 = 0

So , 2 h² - 24 h + 31 h - 372 = 0

Or,  2 h ( h - 12 ) + 31 ( h - 12 ) = 0

Or,   ( h - 12 ) ( 2 h + 31 ) = 0

SO,   h - 12 = 0     And   2 h + 31 = 0

∴     h = 12 yd    And   h =

SO, the Height of triangle = h = 12 yd    and

       The base of triangle = 2 × 12 + 7 = 24 + 7 = 31 yd

        Base = 31 yd

Hence The height of Triangle is 12 yd and The base of Triangle is 31 yd Answer

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step-by-step explanation:

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