ABCD = carré de côté 16cm
BK = x
JC = 10cm
1) CK = BC - BK = 16 - x
2) Aire rectangle = L×l
donc on a :
A(IJCK) = JC×KC
A(IJCK) = 10×(16-x)
A(IJCK) = 160 - 10x
3) Pour x=4
A(IJCK) = 160-10×4 = 160 - 40 = 120cm²
4) A(ABCD) = 16² = 256cm²
On veut que :
A(IJCK) = 1/4 A(ABCD)
160-10x = 1/4 ×256
160-10x = 64
160-64 = 10x
96 = 10x
96/10 = x
9,6 = x