Answer: The height of the triangle is: " 3.5 cm " . _______________________________________________________ <u> Note</u>: The formula/equation for the area, "A" , of a triangle is:
A = (1/2) * b * h ; or write as: A = (b * h) / 2 ; _________________________________________________ in which: "A = area of the triangle" ; "b = base length" ; "h = "[perpendicular] height" ; _________________________________________________ Given: h = (b/2) ; A = 12.25 cm² {Note: Let us assume that the given area was "12.25 cm² " .}. _________________________________________________ We are to find the height, "h" ;
The formula for the Area, "A", is: A = (b * h) / 2 ;
Let us rearrange the formula ; to isolate the "h" (height) on one side of the equation;
→ Multiply EACH side of the equation by "2" ; to eliminate the "fraction" ;
2*A = [ (b * h) / 2 ] * 2 ;
to get: " 2A = b * h " ;
↔ " b * h = 2A " ;
Divide EACH SIDE of the equation by "b" ; to isolate "h" on one side of the equation:
Take the "positive square root" of each side of the equation" ; to isolate "b" on one side of the equation ; & to solve for "b" ;
→ +√(b²) = +√(49 cm²) ;
→ b = 7 cm ;
Now, we want to solve for "h" (the height) : _________________________________________________________ → h = b / 2 = 7 cm / 2 = 3.5 cm ; _________________________________________________________ Answer: The height of the triangle is: " 3.5 cm <span>" . </span>_________________________________________________________