The Soup Shack usually makes tomato soup with 9 tomatoes for every 12 cups of soup. Today, they made 8 cups of soup with 6 tomat
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The base is 16 inches.
The formula for the area of a triangle is
A = 1/2bh
We know that b = h+5, so we can rewrite this as:
A = 1/2(h+5)(h)
Using the area that we have, we now have:
88 = 1/2(h+5)(h)
We can cancel the 1/2 by multiplying by 2:
88*2 = (1/2)(h+5)(h)*2
176 = (h+5)(h)
Using the distributive property, we have:
176 = h² + 5h
We want quadratic equations to be set equal to 0, so we will subtract 176 from both sides:
176 - 176 = h² + 5h - 176
0 = h² + 5h - 176
Using the quadratic formula:
Since a negative length makes no sense, we know that h=11.
The base is 5 inches longer than the height, so b = 11+5 = 16.
The formula for the area of a triangle is
A = 1/2bh
We know that b = h+5, so we can rewrite this as:
A = 1/2(h+5)(h)
Using the area that we have, we now have:
88 = 1/2(h+5)(h)
We can cancel the 1/2 by multiplying by 2:
88*2 = (1/2)(h+5)(h)*2
176 = (h+5)(h)
Using the distributive property, we have:
176 = h² + 5h
We want quadratic equations to be set equal to 0, so we will subtract 176 from both sides:
176 - 176 = h² + 5h - 176
0 = h² + 5h - 176
Using the quadratic formula:
Since a negative length makes no sense, we know that h=11.
The base is 5 inches longer than the height, so b = 11+5 = 16.