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4cm

Step-by-step explanation:

» Concepts

The area of a triangle is how much space is in the triangle. The formula for the area of a triangle is $$\frac{1}{2} bh$$, where b = base and h = height.

» Application

We're given the area as 10 cm² and the base as 5 cm. Thus, we have to plug these values into the formula to solve for the height.

» Solution

- $$10=\frac{1}{2} *5*h$$
- $$10=\frac{5}{2}h$$
- $$10*2/5=5/2(h)*2/5$$
- $$h=4$$
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$$~~~\text{Area of triangle} = \dfrac 12 \times \text{Base} \times \text{Height}\\\\\implies 10 = \dfrac 12 \times 5 \times w\\\\\implies w =\dfrac{20}5 \\\\\implies w = 4 ~cm$$
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